Question

the 19th term of an ap is equal to 3 times its 6 term if its ninth term is 19 find the AP

Answer 1

Given :-

=> a19 = 3(a6)

by formula
=. an = a + ( n - 1) d

n = 19

so,

a19 = a + ( 19 - 1 ) d

a19 = a + 18d

similarly ,

a6 = a + 5d

So,

a + 18d = 3(a + 5d)

a + 18d = 3a +15d

a - 3a + 18d - 15d = 0

- 2a + 3d = 0 ....... ( i )

and


a9 = 19

a + 8d = 19 ...... ( ii ) × 2

adding ( i ) and ( ii ) ×2



-2a +3d +2a +16d = 38

19d = 38

d = 2


Putting the value of d in equation ( ii )


a + 8d = 19

a + 8×2 = 19

a + 16 = 19

a = 19 -16

a = 3


So, to form A.P.

we have formula

=> a , a+d , a+2d

3 , 3 +2 , 3 + 2×2

3 , 5 , 7 is the required A.P.



@Altaf

Answer 2

HELLO DEAR,

GIVEN THAT:-

a19 = 3 x a6

=>a+18d = 3(a+5d)

=>a+18d = 3a +15d

=>3d = 2a

=>a = 3d/2 

=>a9 =19

=>a+8d = 19

=>3d/2 +8d =19

=>19d = 19 x 2

=> d = 2

.....THEREFORE , a = 3d/2 = 3

....................THEREFORE----

3 , 5 , 7 , 9 ,11...........

I HOPE ITS HELP YOU DEAR,
THANKS
REGARDED BY :-) ROHIT KUMAR GUPTA